Linear Classifiers Based on Binary Distributed Representations

Binary distributed representations of vector data (numerical, textual, visual) are investigated in classification tasks. A comparative analysis of results for various methods and tasks using artificial and real-world data is given.

Data Flow Analysis and the Linear Programming Model

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

An Interactive Method of Linear Mixed Integer Multicriteria Optimization

The paper describes a learning-oriented interactive method for solving linear mixed integer problems of multicriteria optimization. The method increases the possibilities of the decision maker (DM) to describe his/her local preferences and at the same time it overcomes some computational difficulties, especially in problems of large dimension. The method is realized in an experimental decision support system for finding the solution of linear mixed integer multicriteria optimization problems.

Classification-Based Method of Linear Multicriteria Optimization

The paper describes a classification-based learning-oriented interactive method for solving linear multicriteria optimization problems. The method allows the decision makers describe their preferences with greater flexibility, accuracy and reliability. The method is realized in an experimental software system supporting the solution of multicriteria optimization problems.

Non-Linear Network-Flow Model of Lukasiewicz’s Multivalue Logic

The paper presents a new network-flow interpretation of Łukasiewicz’s logic based on models with an increased effectiveness. The obtained results show that the presented network-flow models principally may work for multivalue logics with more than three states of the variables i.e. with a finite set of states in the interval from 0 to 1. The described models give the opportunity to formulate various logical functions. If the results from a given model that are contained in the obtained values of the arc flow functions are used as input data for other models then it is possible in Łukasiewicz’s logic to interpret successfully other sophisticated logical structures. The obtained models allow a research of Łukasiewicz’s logic with specific effective methods of the network-flow programming. It is possible successfully to use the specific peculiarities and the results pertaining to the function ‘traffic capacity of the network arcs’. Based on the introduced network-flow approach it is possible to interpret other multivalue logics – of E.Post, of L.Brauer, of Kolmogorov, etc.

Stochastic control strategies and adaptive critic methods

Adaptive critic methods have common roots as generalizations of dynamic programming for neural reinforcement learning approaches. Since they approximate the dynamic programming solutions, they are potentially suitable for learning in noisy, nonlinear and nonstationary environments. In this study, a novel probabilistic dual heuristic programming (DHP) based adaptive critic controller is proposed. Distinct to current approaches, the proposed probabilistic (DHP) adaptive critic method takes uncertainties of forward model and inverse controller into consideration. Therefore, it is suitable for deterministic and stochastic control problems characterized by functional uncertainty. Theoretical development of the proposed method is validated by analytically evaluating the correct value of the cost function which satisfies the Bellman equation in a linear quadratic control problem. The target value of the critic network is then calculated and shown to be equal to the analytically derived correct value.

Operational Methods in the Environment of a Computer Algebra System

This article presents the principal results of the doctoral thesis “Direct Operational Methods in the Environment of a Computer Algebra System” by Margarita Spiridonova (Institute of mathematics and Informatics, BAS), successfully defended before the Specialised Academic Council for Informatics and Mathematical Modelling on 23 March, 2009.

Recursive Methods for Construction of Balanced N-ary Block Designs

2000 Mathematics Subject Classification: Primary 05B05; secondary 62K10.

Method of Linear Programming as an Idea for High School Curriculum

2010 Mathematics Subject Classification: 97D40, 97M10, 97M40, 97N60, 97N80, 97R80

Monte Carlo Algorithms for Linear Problems

MSC Subject Classification: 65C05, 65U05.

Dimension Reduction of the Explanatory Variables in Multiple Linear Regression

2002 Mathematics Subject Classification: 62J05, 62G35.

Comparing Several Methods of Discriminant Analysis on the Case of Wine Data

2000 Mathematics Subject Classification: 62H30, 62J20, 62P12, 68T99

A Refinement of some Overrelaxation Algorithms for Solving a System of Linear Equations

In this paper we propose a refinement of some successive overrelaxation methods based on the reverse Gauss–Seidel method for solving a system of linear equations Ax = b by the decomposition A = Tm − Em − Fm, where Tm is a banded matrix of bandwidth 2m + 1. We study the convergence of the methods and give software implementation of algorithms in Mathematica package with numerical examples. ACM Computing Classification System (1998): G.1.3.

Source localization methods

One of the most pressing demands on electrophysiology applied to the diagnosis of epilepsy is the non-invasive localization of the neuronal generators responsible for brain electrical and magnetic fields (the so-called inverse problem). These neuronal generators produce primary currents in the brain, which together with passive currents give rise to the EEG signal. Unfortunately, the signal we measure on the scalp surface doesn't directly indicate the location of the active neuronal assemblies. This is the expression of the ambiguity of the underlying static electromagnetic inverse problem, partly due to the relatively limited number of independent measures available. A given electric potential distribution recorded at the scalp can be explained by the activity of infinite different configurations of intracranial sources. In contrast, the forward problem, which consists of computing the potential field at the scalp from known source locations and strengths with known geometry and conductivity properties of the brain and its layers (CSF/meninges, skin and skull), i.e. the head model, has a unique solution. The head models vary from the computationally simpler spherical models (three or four concentric spheres) to the realistic models based on the segmentation of anatomical images obtained using magnetic resonance imaging (MRI). Realistic models – computationally intensive and difficult to implement – can separate different tissues of the head and account for the convoluted geometry of the brain and the significant inter-individual variability. In real-life applications, if the assumptions of the statistical, anatomical or functional properties of the signal and the volume in which it is generated are meaningful, a true three-dimensional tomographic representation of sources of brain electrical activity is possible in spite of the ‘ill-posed’ nature of the inverse problem (Michel et al., 2004). The techniques used to achieve this are now referred to as electrical source imaging (ESI) or magnetic source imaging (MSI). The first issue to influence reconstruction accuracy is spatial sampling, i.e. the number of EEG electrodes. It has been shown that this relationship is not linear, reaching a plateau at about 128 electrodes, provided spatial distribution is uniform. The second factor is related to the different properties of the source localization strategies used with respect to the hypothesized source configuration.

A linear relational DEA model to evaluate two-stage processes with shared inputs

Two-stage data envelopment analysis (DEA) efficiency models identify the efficient frontier of a two-stage production process. In some two-stage processes, the inputs to the first stage are shared by the second stage, known as shared inputs. This paper proposes a new relational linear DEA model for dealing with measuring the efficiency score of two-stage processes with shared inputs under constant returns-to-scale assumption. Two case studies of banking industry and university operations are taken as two examples to illustrate the potential applications of the proposed approach.